Currently, recombinant human growth hormone constitutes the only therapy available to children with GH deficiency. This therapy results in a dramatic acceleratin of growth velocity during the first year of therapy then generally slowly declines over subsequent years of treatment. Therapy with rhGH is parenteral and expensive and does not mimic the normal pulsatile pattern of GH release. MK-0677 is an orally active mimetic of the growth hormone-releasing peptides which stimulates pulsatile secretion of GH. This study is intended to provide dose- ranging information for subsequent trials and to assess the safety and efficacy of administering MK-0677 to growth hormone deficient children who have been previously treated with recombinant GH. The hyptheses are that treatment will result in dose-dependent differences in mean growth velocity after 6 months of treatment and MK-0677 will be safe and well tolerated. The objectives are to assess the efficacy and safety and to obtain comparative data to treatment with recombinant GH.